mathematics, the Riemann–Stieltjes integral is a generalization of the Riemann integral, named after Bernhard Riemann and Thomas Joannes Stieltjes. The definition...

known as real analysis, the Riemann integral, created by Bernhard Riemann, was the first rigorous definition of the integral of a function on an interval...

Montel's theorem Riemann–Stieltjes integral Stieltjes constants Stieltjes matrix Stieltjes moment problem Stieltjes polynomials Stieltjes transformation...

framework. The Lebesgue–Stieltjes integral is the ordinary Lebesgue integral with respect to a measure known as the Lebesgue–Stieltjes measure, which may be...

Lebesgue–Stieltjes integral, further developed by Johann Radon, which generalizes both the Riemann–Stieltjes and Lebesgue integrals. The Daniell integral, which...

Similarly, the Stieltjes integral goes back to the Göttinger mathematician, and so they are named together the Riemann–Stieltjes integral. In his habilitation...

central concept is the Itô stochastic integral, a stochastic generalization of the Riemann–Stieltjes integral in analysis. The integrands and the integrators...

Wikipedia page. Length Area Volume Probability Moving average Riemann sum Riemann–Stieltjes integral Bounded variation Jordan content Cauchy principal value...

The Laplace–Stieltjes transform, named for Pierre-Simon Laplace and Thomas Joannes Stieltjes, is an integral transform similar to the Laplace transform...

Riemann–Stieltjes integration. Darboux integrals are named after their inventor, Gaston Darboux (1842–1917). The definition of the Darboux integral considers...

The Riemann zeta function or Euler–Riemann zeta function, denoted by the Greek letter ζ (zeta), is a mathematical function of a complex variable defined...

Henstock–Kurzweil integral or generalized Riemann integral or gauge integral – also known as the (narrow) Denjoy integral (pronounced [dɑ̃ʒwa]), Luzin integral or Perron...

a Riemann–Stieltjes integral). The circle ∘ {\displaystyle \circ } is a notational device, used to distinguish this integral from the Itô integral. Many...

\xi }\,d\mu ,} and called the Fourier-Stieltjes transform due to its connection with the Riemann-Stieltjes integral representation of (Radon) measures....

theorem Riemann–Stieltjes integral Riemann series theorem Riemann sum Riemann–von Mangoldt formula Riemann hypothesis Generalized Riemann hypothesis...

Measure Sigma-algebra Lebesgue space Lebesgue–Stieltjes integration Riemann integral Henstock–Kurzweil integral This approach can be found in most treatments...

same, but using the Riemann–Stieltjes integral, along with an appropriate function of bounded variation, gives a definition of integral equivalent to the...

of the Cauchy–Riemann equations. Note that for smooth complex-valued functions f of compact support on C the generalized Cauchy integral formula simplifies...

q-analogue of the Riemann–Stieltjes integral. Just as the ordinary antiderivative of a continuous function can be represented by its Riemann integral, it is possible...

Partitions are used in the theory of the Riemann integral, the Riemann–Stieltjes integral and the regulated integral. Specifically, as finer partitions of...

\phi } is only assumed to be continuous if the integral is interpreted as a Riemann–Stieltjes integral: ∑ x < n ≤ y a n ϕ ( n ) = A ( y ) ϕ ( y ) − A...

: 13–15  Other integrals can be approximated by versions of the Gaussian integral. Fourier integrals are also considered. The first integral, with broad...

analysis, the Russo–Vallois integral is an extension to stochastic processes of the classical Riemann–Stieltjes integral ∫ f d g = ∫ f g ′ d s {\displaystyle...

corresponding Lebesgue–Stieltjes measure, and the integral with respect to the Lebesgue–Stieltjes measure agrees with the Riemann–Stieltjes integral for continuous...

{R} }\lambda \,\mathrm {d} E_{\lambda }\,.} The integral is understood as a Riemann–Stieltjes integral, convergent with respect to the norm on B(H). In...

bounded, continuous function g: R → R, where the integrals involved are Riemann–Stieltjes integrals. Note that if X and X1, X2, ... are random variables...

the n-th moment of the probability distribution is given by the Riemann–Stieltjes integral μ n ′ = E ⁡ [ X n ] = ∫ − ∞ ∞ x n d F ( x ) {\displaystyle \mu...

bounded on the interval (0, A] for some 0 ≤ α < 1. The q-integral is a Riemann–Stieltjes integral with respect to a step function having infinitely many...

{\displaystyle |X|} is finite, then the expectation is given by the Riemann–Stieltjes integral E [ X ] = ∫ − ∞ ∞ t d F X ( t ) {\displaystyle \mathbb {E} [X]=\int...

against a continuous function can be properly understood as a Riemann–Stieltjes integral: ∫ − ∞ ∞ f ( x ) δ ( d x ) = ∫ − ∞ ∞ f ( x ) d H ( x ) . {\displaystyle...